For any random OS X update that hangs in the dreaded "SoftwareUpdateLauncher" gray screen, do the following:

1. Unplug all external peripherals including secondary monitors
2. At this point the SoftwareUpdaterLauncher should allow the Apple Menu to work.
3. Select the Apple Menu Logout button.
4. Count to five.
5. Click your heels together and repeat: "I want to go back to Kansas Working MacOS"...
6. Take a deep breath and press the Return/Enter key.
7. After a second or so you will see life again: a prompt on whether to Restart or to install and Restart. Since you're here for that update, you might as well choose Install and reboot.
8. Watch it install, and restart.
9. There is no next step. You are done. If not, try the Apple support forums.